Consider a sequence of n 4 independent trials, each resulting in success (S) wit
ID: 3076996 • Letter: C
Question
Consider a sequence of n 4 independent trials, each resulting in success (S) with probability p, and failure (F) with probability 1 - p Say a run of these successes occurs at the beginning of the sequence if the first four trials result in SSSF; a run of three successes occurs at the end of the sequence if the last four trials result in FSSS; and a run of three successes elsewhere in the sequence is the pattern FSSSF. Let R3,n denote the number of runs of three successes in the n trials. Find E(R3,n). Define Rm, n, the number of success runs of length m in n trials, similarly for 1 m n. Find E(Rm, n). Let Rn be the total number of non-overlapping success runs in n trials, counting runs of any length between 1 and n. Find E(Rn) by using the result of b). Find E(Rn) another way by considering for each 1 j n the number of runs that start on the jth trial. Check that the two methods give the same answer.Explanation / Answer
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